Highest Common Factor of 512, 848, 613 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 512, 848, 613 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 848, 613 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 512, 848, 613 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 512, 848, 613 is 1.

HCF(512, 848, 613) = 1

HCF of 512, 848, 613 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 512, 848, 613 is 1.

Highest Common Factor of 512,848,613 using Euclid's algorithm

Highest Common Factor of 512,848,613 is 1

Step 1: Since 848 > 512, we apply the division lemma to 848 and 512, to get

848 = 512 x 1 + 336

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 336 and 512, to get

512 = 336 x 1 + 176

Step 3: We consider the new divisor 336 and the new remainder 176, and apply the division lemma to get

336 = 176 x 1 + 160

We consider the new divisor 176 and the new remainder 160,and apply the division lemma to get

176 = 160 x 1 + 16

We consider the new divisor 160 and the new remainder 16,and apply the division lemma to get

160 = 16 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 512 and 848 is 16

Notice that 16 = HCF(160,16) = HCF(176,160) = HCF(336,176) = HCF(512,336) = HCF(848,512) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 613 > 16, we apply the division lemma to 613 and 16, to get

613 = 16 x 38 + 5

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 5 and 16, to get

16 = 5 x 3 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 613 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(613,16) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 512, 848, 613 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 512, 848, 613?

Answer: HCF of 512, 848, 613 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 848, 613 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 848, 613 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.